2. 1D Motion / Kinematics

Suppose car A starts a race at time $t=0$ with a constant speed $v{a}_0$, and car B starts later at time $t=T$ with a higher constant speed $v{b}_0$ ($v{b}_0>v{a}_0$). How long after car B started the race will car B catch up with car A?

A police car at rest is passed by a speeder traveling at a constant 36 m/s. The police officer takes off in hot

pursuit, accelerating at a constant 2.00 m/s². (a) How long does it take for the police officer to overtake the speeder? (b) Calculate the speed of the police car at the overtaking point.

David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. What is her speed as she passes him?

David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. How far does Tina drive before passing David?

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of $2.80$ m/s². At the same instant a truck, traveling with a constant speed of $20.0$ m/s, overtakes and passes the car. How fast is the car traveling when it overtakes the truck?

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of $2.80$ m/s². At the same instant a truck, traveling with a constant speed of $20.0$ m/s, overtakes and passes the car. How far beyond its starting point does the car overtake the truck?

A cheetah spots a Thomson's gazelle, its preferred prey, and leaps into action, quickly accelerating to its top speed of 30 m/s, the highest of any land animal. However, a cheetah can maintain this extreme speed for only 15 s before having to let up. The cheetah is 170 m from the gazelle as it reaches top speed, and the gazelle sees the cheetah at just this instant. With negligible reaction time, the gazelle heads directly away from the cheetah, accelerating at 4.6 m/s² for 5.0 s, then running at constant speed. Does the gazelle escape? If so, by what distance is the gazelle in front when the cheetah gives up?

A rubber ball is shot straight up from the ground with speed v₀. Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest. What is the maximum value of h for which a collision occurs before the first ball falls back to the ground?

You are 9.0 m from the door of your bus, behind the bus, when it pulls away with an acceleration of 1.0 m/s². You instantly start running toward the still-open door at 4.5 m/s. What is the maximum time you can wait before starting to run and still catch the bus?

A Porsche challenges a Honda to a 400 m race. Because the Porsche's acceleration of 3.5 m/s² is larger than the Honda's 3.0 m/s², the Honda gets a 1.0 s head start. Who wins? By how many seconds?

A rubber ball is shot straight up from the ground with speed v₀. Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest. For what value of h does the collision occur at the instant when the first ball is at its highest point?

Figure 2–55 shows the position vs. time graph for two bicycles, A and B. At which instant(s) are the bicycles passing each other? Which bicycle is passing the other?

(III) A fugitive tries to hop on a freight train traveling at a constant speed of 5.0 m/s. Just as an empty box car passes him, the fugitive starts from rest and accelerates at a = 1.4 m/s² to his maximum speed of 6.0 m/s, which he then maintains. What is the distance traveled to reach the box car?

(II) Two locomotives approach each other on parallel tracks. Each has a speed of 155 km/h with respect to the ground. If they are initially 9.5 km apart, how long will it be before they reach each other? (See Fig. 2–39.)

Figure 2–55 shows the position vs. time graph for two bicycles, A and B. Which bicycle has the larger average velocity?